Toward a generic representation of random variables for machine learning

Marti, Gautier; Very, Philippe; Donnat, Philippe

doi:10.1016/j.patrec.2015.11.004

Cited by 12 publications

(11 citation statements)

References 29 publications

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“…In the clustering literature,[8] make an e ort to overcome this risk by designing a distance measure that incorporates both information from the margins and the dependence structure of the assets.…”

mentioning

confidence: 99%

Portfolio selection based on graphs: Does it align with Markowitz-optimal portfolios?

Hüttner

Mai²,

Mineo³

2018

Dependence Modeling

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Some empirical studies suggest that the computation of certain graph structures from a (large) historical correlation matrix can be helpful in portfolio selection. In particular, a repeated finding is that information about the portfolio weights in the minimum variance portfolio (MVP) from classical Markowitz theory can be inferred from measurements of centrality in such graph structures. The present article compares the two concepts from a purely algebraic perspective. It is demonstrated that this heuristic relationship between graph centrality and the MVP does not originate from a structural similarity between the two portfolio selection mechanisms, but instead is due to specific features of observed correlation matrices. This means that empirically found relations between both concepts depend critically on the underlying historical data. Repeated empirical evidence for a strong relationship is hence shown to constitute a stylized fact of financial return time series.

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mentioning

confidence: 99%

Portfolio selection based on graphs: Does it align with Markowitz-optimal portfolios?

Hüttner

Mai²,

Mineo³

2018

Dependence Modeling

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“…The asymmetry of KL divergence has restricted the application of KL divergence in practical applications. Researchers seek for other divergences in different contexts (e.g., [18], [19], [20]). Pardo surveys a wide range of divergences in his book [2].…”

Section: Related Workmentioning

confidence: 99%

On the Properties of Kullback-Leibler Divergence Between Multivariate Gaussian Distributions

Zhang¹,

Liu²,

Chen³

et al. 2021

Preprint

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Kullback-Leibler (KL) divergence is one of the most important divergence measures between probability distributions. In this paper, we investigate the properties of KL divergence between Gaussians. Firstly, for any two n-dimensional Gaussians N 1 and N 2 , we find the supremum of KL(N 1 ||N 2 ) when KL(N 2 ||N 1 ) ≤ for > 0. This reveals the approximate symmetry of small KL divergence between Gaussians. We also find the infimum of KL(N 1 ||N 2 ) when KL(N 2 ||N 1 ) ≥ M for M > 0. Secondly, for any three n-dimensional Gaussians N 1 , N 2 and N 3 , we find a bound of KL(N 1 ||N 3 ) if KL(N 1 ||N 2 ) and KL(N 2 ||N 3 ) are bounded. This reveals that the KL divergence between Gaussians follows a relaxed triangle inequality. Importantly, all the bounds in the theorems presented in this paper are independent of the dimension n.

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“…Authors leverage the empirical copula transform for several purposes: [6] benefit from its invariance to strictly increasing transformation of X i variables ( Fig. 1) for improving feature selection, [7] to obtain a dependence coefficient invariant with respect to marginal distribution transformations, and [5] to study separately dependence and margins for clustering.…”

Section: The Copula Transformmentioning

confidence: 99%

“…For example, in the specific case of N time series whose observed values are drawn from T independent and identically distributed random variables, one should take into account all the available information in these N time series, i.e. dependence between them and the N marginal distributions, in order to design a proper distance for clustering [5]. Many of the time series datasets which can be found in the lit-erature consist in N real-valued variables observed T times, while in this work we will focus on N × d × T time series datasets, i.e.…”

Section: Introductionmentioning

confidence: 99%

Optimal copula transport for clustering multivariate time series

Marti¹,

Nielsen

Donnat³

2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper presents a new methodology for clustering multivariate time series leveraging optimal transport between copulas. Copulas are used to encode both (i) intra-dependence of a multivariate time series, and (ii) inter-dependence between two time series. Then, optimal copula transport allows us to define two distances between multivariate time series: (i) one for measuring intra-dependence dissimilarity, (ii) another one for measuring inter-dependence dissimilarity based on a new multivariate dependence coefficient which is robust to noise, deterministic, and which can target specified dependencies.

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Toward a generic representation of random variables for machine learning

Cited by 12 publications

References 29 publications

Portfolio selection based on graphs: Does it align with Markowitz-optimal portfolios?

Portfolio selection based on graphs: Does it align with Markowitz-optimal portfolios?

On the Properties of Kullback-Leibler Divergence Between Multivariate Gaussian Distributions

Optimal copula transport for clustering multivariate time series

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